Lecture 1: Introduction

Economics 326 — Introduction to Econometrics II

Author

Vadim Marmer, UBC

What is econometrics?

Econometrics develops statistical methods for:

Estimating economic relationships
Causal or counterfactual analysis: what happens to an outcome when we force a change in a factor.
Testing economic theories
Forecasting important economic variables
Evaluating government and business policy

Why statistics?

Economic theory motivates models of relationships between variables of interest.
Economic models are approximations, not exact descriptions of reality.
Even good models omit important factors that affect outcomes.
We replace a deterministic model with a probabilistic model.

Examples

Estimation of demand and supply functions
Elasticities help evaluate the effects of taxation.
Mincer (1974), Schooling, Experience, and Earnings
Uses individual data to estimate returns to schooling and experience.
- Determine an “optimal” amount of schooling
- Study education in developing countries
- Study gender and race discrimination
- Study the impact of immigration on labour markets

Types of data: cross-section

Definition

A cross-sectional dataset contains observations on individuals (e.g., workers or firms) collected in a single time period.

Example (wages and individual characteristics):

obs	wage	education	experience	female	married
1	3.10	11	2	1	0
2	3.24	12	22	1	1
3	3.00	11	2	0	0
…	…	…	…	…	…

The order of observations is not important.
It is often reasonable to assume observations are statistically independent.

Types of data: time series

Definition

A time series dataset contains observations on one or more variables over time.

Example (Puerto Rico minimum wage, unemployment, and GNP):

obs	year	minimum wage	unemployment	gnp
1	1950	0.20	15.4	878.7
2	1951	0.21	16.0	925.0
3	1952	0.23	14.8	1015.9
…	…	…	…	…

Data frequency can be daily/weekly/monthly/quarterly/annual; in finance, trade data can be very high frequency.
The order of observations is important.
Observations are often correlated (e.g., trends).

Types of data: panel

Definition

A panel dataset combines cross-section and time series: a time series for each cross-sectional unit.

Example (two-year panel on city crime):

obs	city	year	murders	population	unempl	police
1	1	1986	5	350000	8.7	440
2	1	1990	8	359200	7.2	471
3	2	1986	2	64300	5.4	75
4	2	1990	1	65100	5.5	75
…	…	…	…	…	…	…

Causality

We care about causal relationships, but data often only reveal correlations (associations).
To claim a causal effect, other factors affecting the outcome must be held fixed (controlled for).
Controlled experiments help with causality in the natural sciences.
Experiments are often impossible in economics (cost and ethics).
We typically work with observational data.

Examples (causality)

Education

\log(\text{Wage}) = \alpha + \beta \times \text{Years of Schooling} + U

U includes other factors (e.g., ability). If ability is hard to control for, simple correlations can overestimate returns to education.

Police and crime

\text{Number of Crimes} = \alpha + \beta \times \text{Size of the Police Force} + U

Cities with more crime often hire more police, so simple correlations can spuriously suggest police increase crime.

Forecasting vs estimation

Forecasting

Forecasting: predicting out-of-sample values of a variable: E.g.,
- Predict next quarter’s GDP
- Assess the probability of default on a loan given borrower characteristics (income, education, past history of defaults, etc.)
- Predictive text: given previous words, predict the next word.
- ChatGPT: given a prompt, generate the desired response.
- Predict the number of crimes in a city next year given current police force size.
- Forecasting equation: \widehat{\text{Number of Crimes}}= f(\text{Size of the Police Force}) where \widehat{\text{Number of Crimes}} is the forecasted number of crimes in a city with \text{Size of the Police Force}.
- Use data to estimate or “learn” the best forecasting function f(\cdot).
- Focus on prediction accuracy: minimizing some measure of forecast errors.

Estimation

Estimation: estimating structural parameters of an economic model: E.g.,
- Effect of education on wages
- Effect of police force size on crime
- Structural equation: \text{Number of Crimes} = \alpha + \beta \times \text{Size of the Police Force} + U where \beta is the structural parameter measuring the effect of police force size on crime, and U includes other factors affecting crime.
- Focus on causal or counterfactual interpretation: what happens to the outcome when we change a variable.
- Best forecasting model may produce misleading counterfactual effects.
- Good structural model may have poor forecasting performance.
- Choose the right tool for the job!
- Causal/counterfactual analysis always requires some assumptions about the data generating process.

--- title: "Lecture 1: Introduction" subtitle: "Economics 326 — Introduction to Econometrics II" author: - name: "Vadim Marmer, UBC" format: html: output-file: 326_01_intro.html toc: true toc-depth: 3 toc-location: right toc-title: "Table of Contents" theme: cosmo smooth-scroll: true html-math-method: katex pdf: output-file: 326_01_intro.pdf pdf-engine: xelatex geometry: margin=1in fontsize: 11pt number-sections: false toc: false revealjs: output-file: 326_01_intro_slides.html theme: solarized smaller: true slide-number: c/t incremental: true html-math-method: katex scrollable: true chalkboard: false self-contained: true transition: none --- ## What is econometrics? Econometrics develops **statistical methods** for: - **Estimating** economic relationships - **Causal** or **counterfactual** analysis: what happens to an outcome when we force a change in a factor. - **Testing** economic theories - **Forecasting** important economic variables - **Evaluating** government and business policy ## Why statistics? - Economic theory motivates models of relationships between variables of interest. - Economic **models are approximations**, not exact descriptions of reality. - Even good models omit important factors that affect outcomes. - We replace a **deterministic** model with a **probabilistic** model. ## Examples - Estimation of demand and supply functions Elasticities help evaluate the effects of taxation. - Mincer (1974), *Schooling, Experience, and Earnings* Uses individual data to estimate returns to schooling and experience. - Determine an “optimal” amount of schooling - Study education in developing countries - Study gender and race discrimination - Study the impact of immigration on labour markets ## Types of data: cross-section ::: {.callout-note title="Definition"} A **cross-sectional** dataset contains observations on individuals (e.g., workers or firms) collected in a single time period. ::: Example (wages and individual characteristics): | obs | wage | education | experience | female | married | |---:|----:|----------:|-----------:|------:|--------:| | 1 | 3.10 | 11 | 2 | 1 | 0 | | 2 | 3.24 | 12 | 22 | 1 | 1 | | 3 | 3.00 | 11 | 2 | 0 | 0 | | … | … | … | … | … | … | - The order of observations is not important. - It is often reasonable to assume observations are **statistically independent**. ## Types of data: time series ::: {.callout-note title="Definition"} A **time series** dataset contains observations on one or more variables over time. ::: Example (Puerto Rico minimum wage, unemployment, and GNP): | obs | year | minimum wage | unemployment | gnp | |---:|----:|-------------:|-------------:|----:| | 1 | 1950 | 0.20 | 15.4 | 878.7 | | 2 | 1951 | 0.21 | 16.0 | 925.0 | | 3 | 1952 | 0.23 | 14.8 | 1015.9 | | … | … | … | … | … | - Data frequency can be daily/weekly/monthly/quarterly/annual; in finance, trade data can be very high frequency. - The order of observations is important. - Observations are often correlated (e.g., trends). ## Types of data: panel ::: {.callout-note title="Definition"} A **panel** dataset combines cross-section and time series: a time series for each cross-sectional unit. ::: Example (two-year panel on city crime): | obs | city | year | murders | population | unempl | police | |---:|----:|----:|--------:|-----------:|------:|-------:| | 1 | 1 | 1986 | 5 | 350000 | 8.7 | 440 | | 2 | 1 | 1990 | 8 | 359200 | 7.2 | 471 | | 3 | 2 | 1986 | 2 | 64300 | 5.4 | 75 | | 4 | 2 | 1990 | 1 | 65100 | 5.5 | 75 | | … | … | … | … | … | … | … | ## Causality - We care about **causal** relationships, but data often only reveal **correlations** (associations). - To claim a causal effect, **other factors** affecting the outcome must be held fixed (controlled for). - Controlled experiments help with causality in the natural sciences. - Experiments are often impossible in economics (cost and ethics). - We typically work with **observational data**. ## Examples (causality) **Education** $$ \log(\text{Wage}) = \alpha + \beta \times \text{Years of Schooling} + U $$ $U$ includes other factors (e.g., **ability**). If ability is hard to control for, simple correlations can **overestimate** returns to education. **Police and crime** $$ \text{Number of Crimes} = \alpha + \beta \times \text{Size of the Police Force} + U $$ Cities with more crime often hire more police, so simple correlations can **spuriously** suggest police increase crime. # Forecasting vs estimation ## Forecasting - **Forecasting**: predicting **out-of-sample** values of a variable: E.g., - Predict next quarter’s GDP - Assess the probability of default on a loan given borrower characteristics (income, education, past history of defaults, etc.) - Predictive text: given previous words, predict the next word. - ChatGPT: given a prompt, generate the desired response. - Predict the number of crimes in a city next year given current police force size. - Forecasting equation: $$ \widehat{\text{Number of Crimes}}= f(\text{Size of the Police Force}) $$ where $\widehat{\text{Number of Crimes}}$ is the forecasted number of crimes in a city with $\text{Size of the Police Force}$. - Use data to estimate or "learn" the best forecasting function $f(\cdot)$. - Focus on **prediction accuracy**: minimizing some measure of forecast errors. ## Estimation - **Estimation**: estimating **structural parameters** of an economic model: E.g., - Effect of education on wages - Effect of police force size on crime - Structural equation: $$ \text{Number of Crimes} = \alpha + \beta \times \text{Size of the Police Force} + U $$ where $\beta$ is the structural parameter measuring the effect of police force size on crime, and $U$ includes other factors affecting crime. - Focus on **causal or counterfactual interpretation**: what happens to the outcome when we change a variable. - Best forecasting model may produce misleading counterfactual effects. - Good structural model may have poor forecasting performance. - Choose the right tool for the job! - Causal/counterfactual analysis always requires some **assumptions** about the data generating process.